Sea-level observations from tide gauges, wave measurements from in situ buoys and remote sensing altimetry have been used to describe and quantify the effects of the storm over the ocean and also to evaluate the performance of the numerical simulations. Wind and atmospheric pressure records have also been recovered from weather stations on the buoys and compared to the atmospheric forcing used to feed the ocean models.

Wave parameters including significant wave height (Hs), wave peak period (Tp) and wave peak direction have been retrieved from four deep-water buoys and two coastal buoys (see Fig. ). All buoys provide near-real time hourly measurements. These observations have been complemented with along-track measurements of Hs from satellite altimetry onboard satellites SARAL/Altika, Cryosat-2, Sentinel 3A and B and Jason-3, with all missions homogenized with respect to the latter and calibrated on in situ buoy measurements. All wave observations have been downloaded from the CMEMS data server.

Hourly tide gauge time series at five stations over the north-western Mediterranean basin are available in near-real time through the Copernicus Marine Environment Monitoring Service (CMEMS, http://marine.copernicus.eu, last access: 23 February 2020). Two more tide gauges providing near-real time sea-level measurements every minute have been obtained from the Balearic Islands Coastal Ocean Observing and Forecasting System (SOCIB, http://www.socib.es/index.php, last access: 23 February 2020). See Fig.  for the locations of these tide gauge stations.

The storm surge and wind waves generated by Storm Gloria over the western Mediterranean have been simulated using the SCHISM model (Semi-implicit Cross-scale Hydroscience Integrated System Model; ). We have used its dynamic core, which is a derivative product built from the original SELFE (v3.1dc; ), in 2DH barotropic mode fully coupled with the spectral wave model WWM-III . The two modules share the same triangular unstructured computational grid that covers the whole western Mediterranean basin (Fig. ) with a total of 390 113 nodes distributed in 771 297 elements. Its horizontal grid resolution ranges from ∼15 km in the open ocean down to 1–2 km along most coastlines and ∼30 m at the Ebro Delta. This small region covering the Delta and its surroundings contains around 75 % of the grid nodes. The Strait of Gibraltar, the region between Tunisia and Sicily and the Strait of Messina were considered closed boundaries. The model was implemented using the bathymetry 2018 version of the EMODnet digital terrain model (https://portal.emodnet-bathymetry.eu/, last access: 24 January 2020), with a resolution of 1/16×1/16 arc min (∼115m×115 m) over the European sea regions. In the Ebro Delta (upper-left panel in Fig. ) this bathymetry was combined with a high-resolution topography, provided by the Institut Cartogràfic de Catalunya, derived from lidar observations. The product covers an area of 24km×30km with a spatial grid resolution of 2 m. The modelled time period covered 9 d, from 17 to 26 January 2020. The computational time step was set to 10 min and the variables were saved every 30 min. The simulation took a total of 2 d and 19 h and it ran in a single core, which makes a performance of 3.2 times faster than the real time.

The atmospheric fields used to force SCHISM were retrieved from the high-resolution version of the deterministic ECMWF analysis (https://www.ecmwf.int/en/forecasts/datasets/set-i, last access: 29 January 2020). These analyses are provided on a regular lat–long grid and have the highest currently available ECMWF horizontal grid resolution (0.1∘×0.1∘), which is roughly equivalent to 9 km at the mid latitudes. In terms of temporal resolution, the outputs are available every 6 h, i.e. at 00:00, 06:00, 12:00 and 18:00 UTC. The atmospheric forcing terms correspond to the mean sea-level atmospheric pressure, the U component and V component of the wind at 10 m, spanning the period 6–27 January. We have compared point-wise modelled time series with measurements of the atmospheric parameters over the ocean at buoy locations (see the section above for details on the stations) in Fig. S1. The results show good agreement at every location and for all the forcing terms, thus confirming the reliability of the atmospheric forcing fields. Tides were not considered in the simulation since the western Mediterranean is a micro-tidal environment.

In order to evaluate the contribution of the different forcing factors, namely atmospheric pressure, wind and wave setup, to the total water levels along the coasts, four different simulations were designed: (1) a fully coupled run between the hydrodynamic model and the wind-wave module that takes into account all the forcings as well as their coupling; (2) a run without wind waves, using only the hydrodynamic module forced by wind and atmospheric pressure; (3) a hydrodynamic model run forced only by atmospheric pressure; and (4) a hydrodynamic model run forced only by wind. The total storm surge generated by Storm Gloria was evaluated using only simulation no. 1; the effect of the wind waves and the coupling with the dynamic effects was estimated by the difference between run nos. 1 and 2; finally, the contribution of the atmospheric pressure (wind) was determined with run 3 (4). To quantitatively determine the individual effect as well as the synergistic effect between a set of different factors, a total of (2no.offorcings) simulations are required , with all the possible combinations of switching on and off all the forcing terms. However, if the difference between the fully coupled run (no. 1) and the combination of the different forcings [(no. 1 - no. 2) + no. 3 + no. 4] is computed, the median relative difference emerging from the simulations is around 0 % and the maximum relative difference at one coastal point is around 3 %. These small differences indicate that the interaction between the different forcings is small and justifies not performing the additional numerical simulations. Note that even in the absence of strong interaction between storm surge waves and wind waves, the coupled simulation is needed to account for the effects of the wave setup along the coasts.

To explore the impacts of Storm Gloria at the local scale, we focus on two cases under different forcing conditions. In the first one, we quantify the flooding induced by the joint effect of storm surges and waves on the Ebro Delta, taking advantage of the local very high grid resolution that allows an accurate representation of the local topographic features. In the second case, we evaluate the nearshore wave propagation and overtopping in Portocolom, located on the eastern coast of Mallorca (Fig.  and upper panel in Fig. ), a rocky coast formed by high cliffs (∼15 m) where numerous damages were reported by waves overtopping. Note that spectral wave models, such as the WWM-III model used here, are unable to represent the overtopping generated by individual ocean waves; therefore, a set of 1-D simulations was performed with the non-hydrostatic phase-resolving model SWASH (; http://swash.sourceforge.net/, last access: 9 March 2020) along a bathymetric profile with 1 m of horizontal resolution extracted from a nautical chart (1:5000) from the Spanish Army Hydrographic (IHM) Institute (the location of the profile is indicated by a red line in the upper panel in Fig. ; the profile is shown in the lower inset in the upper panel in Fig. ). The left-hand side of the profile was artificially set as downhill in order to account for all the water that overtops the cliff (upper inset in Fig. ). The Manning roughness coefficient was considered constant in all the domain with a value of 0.025. The wave forcing provided by the closest grid point of the regional model (extracted from simulation no. 1) was introduced on the eastern side of the 1-D domain with a JONSWAP spectrum. With this configuration, the simulation time was 60 min, with an initial computation time step of 0.05 s. Given that the comparison between modelled and observed Hs at the nearest buoy (Mahon) suggests that the model underestimates the magnitude of the waves (see Sect. ), instead of using the time series of wave parameters of the closest point, a set of values for Hs have been tested, ranging from 5 to 10 m, every 0.5 m, to determine the minimum significant wave height needed to have overtopping on the cliffs. To minimize the inherent stochasticity when generating the wave forcing with a JONSWAP spectrum, a total of 100 simulations with different seeds to generate the spectra were run for each Hs analysed.

Modelled storm surges and waves have been compared to observations for the period 17–26 January 2020. The time series of the closest model grid point (the distance between model grid point and observation is indicated in Fig. ) was extracted for comparison with in situ measurements. For the comparison to altimetry data, the closest model grid point in space, but also in time, to each altimetry track was used. Satellite observations with distance larger than 10 km from the closest grid point or with a time difference larger than 15 min between modelled time and observed time were discarded.

Figure  displays the comparison between modelled and observed wave parameters. In situ measurements of Tp and wave direction are very well captured by the model output at both deep-water and coastal wave buoys. During the storm, Tp ranges between 10 and 12 s everywhere, with directions from the west (∼90∘). Changes in these parameters are correctly simulated during the entire period with maximum differences in Tp of only 1 s. Hs significantly increases during the storm, reaching values of up to 8 m, according to observations. The model underestimates Hs at all buoy locations, except in the two buoys near Tarragona (light blue curves in Fig. ). Differences between model and observations for Hs are between 1 m in Valencia (dark blue line) and 2.5 m in Mahon (red line) during the peak of the storm. This underestimation is also found consistently in the comparison to altimetry. The scatter plot of along-track altimetric observations and the corresponding model results displays a significant correlation of 0.73, although with a slope between observed and modelled Hs of 0.90, indicating that the overall underestimation is about 10 % of Hs over the western Mediterranean basin. The possible causes of this underestimation include a poor energy transfer between the atmosphere and the ocean as simulated by the WWM-III wave model, a limited atmospheric forcing (either in terms of temporal or spatial resolution), and inaccurate bathymetry in some locations. To discard the role of the wave model in the Hs underestimation, we repeated the wave simulation with the same computational grid using the SWAN model, a different spectral wave model developed at Delft University of Technology (http://swanmodel.sourceforge.net/, last access: 9 March 2020) which led to equivalent results. As discussed above in the previous section, Fig. S1 shows a good agreement between observations of atmospheric pressure and winds and the model forcing, with only small underestimations in wind velocity during the peak of the storm. Thus, we conclude that the likely causes of the Hs underestimation are related to limited bathymetry and small inaccuracies in the atmospheric forcing fields.

Coastal sea surface elevation is compared in Fig.  to tide gauge observations. Time series are referred to mean sea level at each site. The sea-level time series recorded by the tide gauges (represented in different colours in Fig.  panels) have been detided (using the complete record of each station) and low-pass filtered using a Butterworth filter with a cutoff period of 30 min to remove the resonant modes of the harbours where the tide gauges are located. The filtered non-tidal residuals were compared to modelled outputs at grid points located within a radius of 2.5 km from the tide gauge. This approach seeks to minimise the effect of local topographic features in the differences between modelled and observed records. We recall here that, since we run the coupled version of the model, sea surface elevation accounts for the storm surge and the effect of wave setup (every contributor is discussed and quantified below). Notably, observations indicate that sea levels have temporarily risen for up to 70 cm along the coasts in the mainland (sea level rises up 1 m in Gandia prior to detiding and filtering – not shown). In contrast, values are much lower (around 20 cm) at tide gauges in the Balearic Islands. The similarities between modelled and observed extreme sea levels are remarkable at every tide gauge station: in Gandia, Sagunto and Valencia, the locations with larger increases, the model mimics both the intensity and the evolution of the sea surface elevation. Only in the tide gauge station in Tarragona is the model found to significantly underestimate (∼15 cm) observed sea levels; for the rest of the tide gauge records, the model results follow the oscillations and their magnitudes observed by the instruments. The underestimation of ocean surface elevation observed in Tarragona is likely related to inaccurate bathymetry at this location, a factor to which the storm surges are more sensitive at coastal locations.

The overall good agreement between modelled and observed sea level, as measured by tide gauges, suggests that the simulation correctly captures the most relevant processes that are taking place during Storm Gloria. In particular, the contribution of the wave setup can be quantified by comparing observations to both coupled and uncoupled runs. This is shown for the tide gauge in Gandia in Fig. S3. Not accounting for the wave setup (red lines) underestimates by around 20 cm the observed sea level (blue line), whereas including the effect of waves (grey lines) decreases this bias. Indeed, the closest grid point (thick grey line) mimics the amplitude of the observed storm surge when including the effect of waves. This indicates that the spatial resolution along the coast (∼1–2 km at this site) is enough to represent the effects of the wave setup.

Shortly after Storm Gloria, Copernicus EMS produced and published an image based on Sentinel-1 satellite observations of the flooded area in the Ebro Delta, one of the regions most impacted by the storm (image available at http://floodlist.com/europe/spain-storm-gloria-floods-january-2020, last access: 9 March 2020). The satellite image maps the flooding during the days 20–22 January and shows the extensive and striking devastation over most of the delta region. Note, however, that the image does not discriminate between coastal storm surge and rain-induced flooding and that such discrimination is important for differentiating the parts flooded by salty water from those flooded by freshwater, as their impacts are very different, especially for agricultural areas.

Our numerical simulation provides the total flooded area over the high-resolution Ebro Delta topography induced by the storm surge and waves. The results, mapped in Fig. , show the maximum modelled flooding during Storm Gloria from 17 to 26 January that reaches up to 4 km inland. This value is comparable to the 3 km extend reported by Copernicus EMS: “a storm surge also swept 3 km inland, devastating rice paddies and coastal features in the Ebro river delta …” (at https://emergency.copernicus.eu/mapping/ems/copernicus-emergency-management-service-monitors-impact-flood-spain, last access: 9 March 2020). The satellite image indicates that the extension of the flooding caused by the storm was larger than that obtained in our simulation. We explain this apparent discrepancy by the fact that we do not account for the flooding caused by the heavy rains that were reported in the area; instead, our results identify the extent of the flooding caused solely by the marine hazards. Notably, it is worth mentioning that our simulation reproduces the complete flooding of the Trabucador bar, which was swept out by the hazard.

We recall here that the validation of the model outputs indicated that the predicted storm surge in the Tarragona tide gauge, the closest station to the delta, was underestimated (Fig. ). Therefore, our simulation could be considered a lower bound for the flooded area.

Another location that was severely hit by Storm Gloria was Portocolom, located on the eastern coast of Mallorca (see Fig.  for the location; top panel Fig. ). This section of the coastline, formed by high cliffs (∼15 m), was impacted by large waves that overtopped the cliffs and whose spray reached up to 30 m high (see the inset picture in the lower panel in Fig. ). It caused damages to properties and temporary evacuation of the population.

Our regional simulation provides small storm surge values in the Balearic Islands (Fig. b), in contrast to the large surges found along the coastline of the mainland. It also provides a maximum Hs of around 4.5 m in the vicinity of Portocolom during the storm (Fig. a). The SWASH model has been implemented in 1-D in a section normal to the coast of Portocolom (red line in the upper panel and the insets from Fig. ), as described in the methodology in Sect. . The initial tests indicated that the modelled Hs of 4.5 m is not high enough as to produce any overtopping. This is not surprising, since modelled Hs underestimates the maximum value recorded by the buoy at Mahon, located in the same area, by an amount of 2.5 m (21 January at 12:00; red spot in Fig. ); thus, it is likely that the value in Portocolom is also biased low. Therefore, given that there are a number of visual confirmations that overtopping was produced in this section of the cliffs (see the list in the Appendix, for example), we designed a set of SWASH simulations with values of Hs ranging from 5 up to 10 m with a step of 0.5 m and fixing the peak period to 13 s (this is the value estimated by our regional simulation). For each value of Hs, we run 100 1-D SWASH simulations, of 60 min each, along the same bathymetric profile to account for the inherent variability in wave height. The averaged water flux over the cliffs and the number of waves that overtopped were computed in every run. These results are represented by the green and orange box plots, respectively, in the lower panel of Fig. . It can be seen that the first set of 100 simulations that shows overtopping corresponds to a Hs of 7 m. This result suggests that our model is underestimating, at least, around 2.5 of Hs, in line with the comparison with observations in the buoy from Mahon (Fig. ). Then, as expected, the value of the flux and the number of waves that overtopped the cliffs increase with Hs. As an example, when Hs is 8.5 m, the amount of water over the 15 m cliffs is ∼3600 L per hour and metre. Note that our values do not account for the water input from the spray which, according to observations, was the most damaging to coastal properties, mostly related to the impact of the wave water column against house roofs and balconies.